CN112230195A - Smoothing variable structure filtering method and system based on nonlinear optimal smoothing layer strategy - Google Patents

Smoothing variable structure filtering method and system based on nonlinear optimal smoothing layer strategy Download PDF

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CN112230195A
CN112230195A CN202010911596.6A CN202010911596A CN112230195A CN 112230195 A CN112230195 A CN 112230195A CN 202010911596 A CN202010911596 A CN 202010911596A CN 112230195 A CN112230195 A CN 112230195A
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李刚
李耀文
刘瑜
何友
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Naval Aeronautical University
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Abstract

The application discloses a smooth variable structure filtering method and a system based on a nonlinear optimal smooth layer strategy, wherein the method comprises the following steps: calculating nonlinear optimal smooth layer parameters in real time under the minimum mean square error criterion based on a nonlinear switching function; comparing the nonlinear optimal smooth parameter with a preset smooth layer parameter to judge the uncertainty of the current model; calculating a gain term by adopting a self-adaptive switching strategy according to the uncertainty, and calculating a target state estimation value in a frame of prior prediction-posterior updating by utilizing the gain term; the above process is iterated sequentially to achieve continuous tracking of the target state. The method adopts a self-adaptive switching strategy based on nonlinear optimal smooth layer parameters to calculate the gain item, can realize the optimality of a tracking algorithm and a tracking system under low model uncertainty, and simultaneously ensures the robustness and excellent buffeting suppression characteristic under high uncertainty, thereby obtaining better target state tracking precision and having higher engineering application value.

Description

Smoothing variable structure filtering method and system based on nonlinear optimal smoothing layer strategy
Technical Field
The application relates to the technical field of radars, in particular to a smoothing variable structure filtering method and a system based on a nonlinear optimal smoothing layer strategy for radar target tracking under the condition of model uncertainty.
Background
The radar target tracking system continuously and effectively estimates the number, position, speed, acceleration and other motion states of targets by using the information of target distance, azimuth angle, Doppler frequency offset and the like contained in radar echoes. The radar tracking system is widely applied to the fields of automatic driving, air traffic control, meteorological monitoring, security, national defense and military and the like. State estimation, i.e. filtering, is an important link for radar tracking. Traditional bayesian estimation methods, such as Kalman Filtering (KF), Extended Kalman Filtering (EKF), insensitive kalman filtering (UKF), Particle Filtering (PF), etc., are built on system state equations and measurement equations of state space, relying on accurate description of the target motion model. If the deviation between the system state equation and the real target motion is large, for example, the target generates strong maneuvering motion, the tracking error is increased sharply, and even the filtering divergence loses the target, namely, the model is uncertain.
Smooth Variable Structure Filtering (SVSF) is a robust filtering method under The condition of model uncertainty, and based on a slip film control theory and a variable structure control method (see The related art 1: S. Habibi, "The smooth variable structure filter," Proceedings of The IEEE, vol.95, No.5, pp.1026-1059, May,2007.), The method can ensure The boundedness of state estimation errors. The method adopts the framework of prior estimation-posterior updating of classic Bayes filtering and introduces a gain term based on a switching function and a smoothing layer parameter. The smoothing layer parameters are defined as the upper bound of model uncertainty. The ratio of the observation innovation to the smoothing layer parameters is used to reflect the magnitude of the current model error and is used as the input of the switching function to control the norm of the gain term.
Smooth variable structure filtering mainly has two problems: buffeting problems and parameter sensitivity. The buffeting problem is that the gain term contains observation information, so that the gain term is disturbed by random observation errors, and misjudgment is generated on the error amplitude of a real model (see related technology 1). The problem of chattering causes a rapid decrease in tracking accuracy, and particularly in the dimension of a state such as velocity and acceleration which cannot be directly observed. The problem of buffeting is increasingly severe in cases of high model uncertainty and strong observation noise. The buffeting phenomenon can be relieved by adopting a nonlinear and smooth switching function, such as a hyperbolic tangent function (see the related technology 2: Ligang, Liyan, Liuyu, who friend. smooth variable structure filtering method and system based on a modified switching function [ P ]. Beijing City: CN109444841A, 2019-03-08.); these methods still suffer from parameter sensitivity problems. The parameter sensitivity problem means that the performance of the filter depends heavily on the preset smoothing layer parameter, and the parameter is often set empirically and is inaccurate. If the preset parameters of the smooth layer are too small, the buffeting problem is aggravated; if the preset smoothing layer parameters are too large, the robustness of the filter to modeling errors is lost and even filter divergence is caused (see correlation 1 and correlation 3, correlation 3: M.Attari, Z.Luo, and S.Habibi, "An SVSF-based generated robust protocol for target tracking in client," IEEE Transactions on Intelligent transfer Systems, vol.17, No.5, 138. 1-1392, May, 2016.). By minimizing the a posteriori state estimation covariance, adaptive smoothing layer parameters can be obtained, which have optimality under low model uncertainty conditions (see related art 3); however, these methods are based on piecewise linear switching functions and thus still suffer from buffeting.
Therefore, how to design the calculation criterion of the gain term, while ensuring the robustness, the buffeting problem and the parameter sensitivity problem are solved, so as to improve the performance of radar target state estimation, which is a problem to be solved urgently in engineering application of SVSF.
Content of application
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, one purpose of the invention is to provide a smoothing variable structure filtering method based on a nonlinear optimal smoothing layer strategy, which can significantly improve the accuracy of radar target state estimation, ensure the filtering robustness under the condition of model uncertainty and have good application value.
Another objective of the present invention is to provide a smooth variable structure filtering system based on a nonlinear optimal smoothing layer strategy.
In order to achieve the above object, an embodiment of the present invention provides a smooth variable structure filtering method based on a nonlinear optimal smoothing layer strategy, including the following steps: calculating nonlinear optimal smooth layer parameters in real time under the minimum mean square error criterion based on a nonlinear switching function; comparing the nonlinear optimal smooth parameter with a preset smooth layer parameter to judge the uncertainty of the current model; and calculating a gain term by adopting a self-adaptive switching strategy according to the uncertainty of the current model, and calculating a target state estimation value in a priori prediction-posterior updating frame by utilizing the gain term.
According to the smoothing variable structure filtering method based on the nonlinear optimal smoothing layer strategy, the gain item is calculated by adopting the adaptive switching strategy based on the nonlinear optimal smoothing layer parameters, so that the optimality of a tracking algorithm and a system under low model uncertainty can be realized, and meanwhile, the robustness under high uncertainty and excellent buffeting suppression characteristics are ensured, so that better target state tracking accuracy is obtained, and the method has higher engineering application value.
In addition, the smooth variable structure filtering method based on the nonlinear optimal smoothing layer strategy according to the above embodiment of the present invention may further have the following additional technical features:
further, in an embodiment of the present invention, the calculation formula of the nonlinear optimal smoothing layer parameter is:
Figure BDA0002663486760000021
Figure BDA0002663486760000022
Figure BDA0002663486760000031
wherein artan (-) is an inverse hyperbolic tangent function defined on each element of the matrix;
Figure BDA0002663486760000032
indicating the k +1 th frame radar measurement matrix
Figure BDA0002663486760000033
The full-rank blocking submatrix of (1), wherein m and n are the dimensions of the system state variable and the observation variable, respectively;
Figure BDA0002663486760000034
and
Figure BDA0002663486760000035
is a block submatrix of a prior state estimation error covariance matrix P (k +1| k); e.g. of the typez(k +1| k) is the observation innovation term; s (k +1) is an innovation covariance matrix; ezAnd EyIs a mixing error term;
Figure BDA0002663486760000036
is to the state transition matrix
Figure BDA0002663486760000037
Transformation state transition matrix after introduction of transformation matrix T
Figure BDA0002663486760000038
Representing the main diagonal element as a diagonal matrix of vector a.
Further, in an embodiment of the present invention, comparing the nonlinear optimal smoothing parameter with a preset smoothing layer parameter to determine a magnitude of uncertainty of the current model, further includes:
when t isNGVBL>ΨmaxThen, the uncertainty of the current model is determined to be highModel uncertainty, whereNGVBLFor a non-linear optimal smoothing layer parameter, ΨmaxThe parameters are preset smooth layer parameters;
when t isNGVBL≤ΨmaxAnd judging the uncertainty of the current model as the low model uncertainty.
Further, in an embodiment of the present invention, an adaptive handover strategy is used to calculate the gain term according to the uncertainty of the current model, further comprising:
under the condition of low model uncertainty, the calculation formula of the gain term is as follows:
Figure BDA0002663486760000039
Figure BDA00026634867600000310
Figure BDA00026634867600000311
under the condition of high model uncertainty, the calculation formula of the gain term is as follows:
K(k+1)＝KNGVBL，
KNGVBL＝P(k+1|k)H(k+1)TS(k+1)-1。
further, in an embodiment of the present invention, the calculating the target state estimation value in a framework of a priori prediction-a posteriori updating using the gain term comprises: target state variable at time k-0
Figure BDA00026634867600000312
And the covariance P (0|0) of the state estimation is used as initialization data, and the state variable at the moment of k +1 and the posterior estimation of the covariance matrix thereof are calculated in an iterative way
Figure BDA0002663486760000041
And P (k +1| k +1), k ═ k0,1,2, … until the radar system judges that the track is finished, the concrete steps are as follows:
1) calculating the prior estimation of the target state at the k +1 moment based on a preset target motion model and a radar measurement model
Figure BDA0002663486760000042
Radar measurement prior estimation
Figure BDA0002663486760000043
And a prior state estimation covariance matrix P (k +1| k):
Figure BDA0002663486760000044
Figure BDA0002663486760000045
Figure BDA0002663486760000046
wherein the content of the first and second substances,
Figure BDA0002663486760000047
and u is the control input matrix and control input variable, Q is the process noise covariance;
2) and (3) calculating a priori measurement error by using a target measurement z (k +1) scanned by the radar at the k +1 moment:
Figure BDA0002663486760000048
calculating a blending error term using ez(k | k) represents the posterior measurement error at time k ·ABSMeans taking the absolute value element by element for the vector,
Figure BDA0002663486760000049
and
Figure BDA00026634867600000410
is an attenuation factor with a value in the interval (0, 1):
Figure BDA00026634867600000411
Figure BDA00026634867600000412
calculating a new information covariance matrix S (k + 1):
S(k+1)＝H(k+1)P(k+1|k)H(k+1)T+R(k+1)，
substituting a priori measurement error calculation formula, a mixed error term calculation formula and an innovation covariance matrix calculation formula into a self-adaptive switching strategy to calculate a gain term K (K + 1);
3) calculating the posterior estimation of the target state by using each item of prior predicted value in 1) and gain item K (K +1) in 2)
Figure BDA00026634867600000413
And a posterior state estimation covariance matrix P (k +1| k + 1):
Figure BDA00026634867600000414
P(k+1|k+1)＝[I-K(k+1)H(k+1)]P(k+1|k)[I-K(k+1)H(k+1)]T+K(k+1)R(k+1)K(k+1)Twherein the content of the first and second substances,
Figure BDA00026634867600000415
is a unit matrix and R represents the measurement noise covariance.
In order to achieve the above object, another embodiment of the present invention provides a smooth variable structure filtering system based on a nonlinear optimal smoothing layer strategy, including: the first calculation module is used for calculating nonlinear optimal smooth layer parameters in real time under the minimum mean square error criterion based on a nonlinear switching function; the comparison module is used for comparing the nonlinear optimal smooth parameter with a preset smooth layer parameter so as to judge the uncertainty of the current model; and the second calculation module is used for calculating a gain term by adopting a self-adaptive switching strategy according to the uncertainty of the current model and calculating the estimated value of the target state in a frame of prior prediction-posterior update by utilizing the gain term.
According to the smoothing variable structure filtering system based on the nonlinear optimal smoothing layer strategy, the gain item is calculated by adopting the adaptive switching strategy based on the nonlinear optimal smoothing layer parameters, so that the optimality of a tracking algorithm and the system under low model uncertainty can be realized, and meanwhile, the robustness under high uncertainty and excellent buffeting suppression characteristics are ensured, so that better target state tracking accuracy is obtained, and the system has higher engineering application value.
In addition, the smooth variable structure filtering system based on the nonlinear optimal smoothing layer strategy according to the above embodiment of the present invention may further have the following additional technical features:
further, in an embodiment of the present invention, the calculation formula of the nonlinear optimal smoothing layer parameter is:
Figure BDA0002663486760000051
Figure BDA0002663486760000052
Figure BDA0002663486760000053
wherein artan (-) is an inverse hyperbolic tangent function defined on each element of the matrix;
Figure BDA0002663486760000054
indicating the k +1 th frame radar measurement matrix
Figure BDA0002663486760000055
Of full rank partitioned submatrices, where m sumsn is the dimension of the system state variable and the observation variable respectively;
Figure BDA0002663486760000056
and
Figure BDA0002663486760000057
is a block submatrix of a prior state estimation error covariance matrix P (k +1| k); e.g. of the typez(k +1| k) is the observation innovation term; s (k +1) is an innovation covariance matrix; ezAnd EyIs a mixing error term;
Figure BDA0002663486760000058
is to the state transition matrix
Figure BDA0002663486760000059
Transformation state transition matrix after introduction of transformation matrix T
Figure BDA00026634867600000510
Representing the main diagonal element as a diagonal matrix of vector a.
Further, in an embodiment of the present invention, the comparison module is further configured to determine when ΨNGVBL>ΨmaxWhen the model uncertainty is high, the uncertainty of the current model is judged to be high, wherein psiNGVBLFor a non-linear optimal smoothing layer parameter, ΨmaxThe parameters are preset smooth layer parameters; when t isNGVBL≤ΨmaxJudging the uncertainty of the current model as low model uncertainty;
under the condition of low model uncertainty, the calculation formula of the gain term is as follows:
Figure BDA0002663486760000061
Figure BDA0002663486760000062
Figure BDA0002663486760000063
under the condition of high model uncertainty, the calculation formula of the gain term is as follows:
K(k+1)＝KNGVBL，
KNGVBL＝P(k+1|k)H(k+1)TS(k+1)-1。
further, in an embodiment of the present invention, the second calculating module is further configured to target the state variable at the time when k is 0
Figure BDA0002663486760000064
And the covariance P (0|0) of the state estimation is used as initialization data, and the state variable at the moment of k +1 and the posterior estimation of the covariance matrix thereof are calculated in an iterative way
Figure BDA0002663486760000065
And P (k +1| k +1), k being 0,1,2, …, until the radar system determines that the track is finished, specifically including:
1) calculating the prior estimation of the target state at the k +1 moment based on a preset target motion model and a radar measurement model
Figure BDA0002663486760000066
Radar measurement prior estimation
Figure BDA0002663486760000067
And a prior state estimation covariance matrix P (k +1| k):
Figure BDA0002663486760000068
Figure BDA0002663486760000069
Figure BDA00026634867600000610
wherein the content of the first and second substances,
Figure BDA00026634867600000611
and u is the control input matrix and control input variable, Q is the process noise covariance;
2) and (3) calculating a priori measurement error by using a target measurement z (k +1) scanned by the radar at the k +1 moment:
Figure BDA00026634867600000612
calculating a blending error term using ez(k | k) represents the posterior measurement error at time k ·ABSMeans taking the absolute value element by element for the vector,
Figure BDA00026634867600000613
and
Figure BDA00026634867600000614
is an attenuation factor with a value in the interval (0, 1):
Figure BDA00026634867600000615
Figure BDA00026634867600000616
calculating a new information covariance matrix S (k + 1):
S(k+1)＝H(k+1)P(k+1|k)H(k+1)T+R(k+1)，
substituting a priori measurement error calculation formula, a mixed error term calculation formula and an innovation covariance matrix calculation formula into a self-adaptive switching strategy to calculate a gain term K (K + 1);
3) calculating the posterior estimation of the target state by using each item of prior predicted value in 1) and gain item K (K +1) in 2)
Figure BDA0002663486760000071
Covariance matrix of a posteriori state estimatesP(k+1|k+1)：
Figure BDA0002663486760000072
P(k+1|k+1)＝[I-K(k+1)H(k+1)]P(k+1|k)[I-K(k+1)H(k+1)]T+K(k+1)R(k+1)K(k+1)TWherein the content of the first and second substances,
Figure BDA0002663486760000073
is a unit matrix and R represents the measurement noise covariance.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of a smoothing variable structure filtering method based on a nonlinear optimal smoothing layer strategy according to an embodiment of the present invention;
FIG. 2 is a flowchart illustrating the operation of a smoothing variable structure filtering method based on a non-linear optimal smoothing layer strategy according to an embodiment of the present invention;
FIG. 3 is a simulation scene example of the tracking of a vehicle target by a 2-D millimeter wave radar in an autonomous driving scene according to an embodiment of the invention;
FIG. 4 is a schematic diagram of the change of the target state estimation error with time compared with the conventional method according to the embodiment of the present invention, in FIG. 4, (a) an X coordinate estimation error, (b) a Y coordinate estimation error, (c) an X direction velocity estimation error, and (d) a Y direction velocity estimation error;
FIG. 5 is a schematic diagram showing the variation of buffeting suppression effect over time for a comparison of the method of the present invention with a conventional method in a simulation scenario according to an embodiment of the present invention, where in FIG. 5, (a) X-coordinate buffeting amplitude, and (b) Y-coordinate buffeting amplitude;
fig. 6 is a schematic structural diagram of a smoothing variable structure filtering system based on a nonlinear optimal smoothing layer strategy according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The invention aims to synergistically overcome the buffeting problem and the parameter sensitivity problem of the conventional smooth variable structure filtering method, provides a smooth variable structure filtering method based on a nonlinear optimal smooth layer strategy, solves the robust tracking problem under the uncertain condition of a target motion model, is applied to a radar target tracking system, is used for target state estimation of the radar system, and belongs to the field of radar data processing. The non-linearity means that the self-adaptive smooth layer parameters derived by the method are based on a non-linear switching function (hyperbolic tangent function) and have a non-linear form, and the optimal means that the self-adaptive smooth layer parameters have optimality in the meaning of minimum mean square error. The method is based on a nonlinear switching function, a nonlinear optimal smooth layer parameter is calculated in real time under the minimum mean square error criterion, the parameter is used for realizing a self-adaptive switching strategy to calculate a gain item, the parameter optimality is realized under the condition of low model uncertainty, and the filtering robustness and the effective buffeting suppression effect can be ensured under the condition of high model uncertainty.
The following describes a smooth-varying structure filtering method and system based on a nonlinear optimal smooth layer strategy according to an embodiment of the present invention with reference to the drawings, and first, a smooth-varying structure filtering method based on a nonlinear optimal smooth layer strategy according to an embodiment of the present invention will be described with reference to the drawings.
Fig. 1 is a flowchart of a smoothing variable structure filtering method based on a nonlinear optimal smoothing layer strategy according to an embodiment of the present invention.
As shown in fig. 1, the smooth variable structure filtering method based on the nonlinear optimal smooth layer strategy includes the following steps:
in step S101, nonlinear optimal smoothing layer parameters are calculated in real time under the minimum mean square error criterion based on a nonlinear switching function.
Specifically, a nonlinear optimal smooth layer parameter psi is calculated in real time according to a state equation and an observation equation of a radar tracking systemNGVBL：
Figure BDA0002663486760000081
Figure BDA0002663486760000082
Figure BDA0002663486760000083
Wherein artan (-) is an inverse hyperbolic tangent function defined on each element of the matrix;
Figure BDA0002663486760000084
indicating the k +1 th frame radar measurement matrix
Figure BDA0002663486760000085
The full-rank blocking submatrix of (1), wherein m and n are the dimensions of the system state variable and the observation variable, respectively;
Figure BDA0002663486760000086
and
Figure BDA0002663486760000087
is a block submatrix of a prior state estimation error covariance matrix P (k +1| k); e.g. of the typez(k +1| k) is the observation innovation term; s (k +1) is an innovation covariance matrix; ezAnd EyIs a mixing error term;
Figure BDA0002663486760000091
is to the state transition matrix
Figure BDA0002663486760000092
Transformation state transition matrix after introduction of transformation matrix T
Figure BDA0002663486760000093
Representing the main diagonal element as a diagonal matrix of vector a.
In step S102, the nonlinear optimal smoothing parameter is compared with a preset smoothing layer parameter to determine the uncertainty of the current model.
Specifically, the real-time updated nonlinear optimal smoothing layer parameter Ψ obtained in step S101 is usedNGVBLWith predetermined smoothing layer parameters (here psi)maxRepresentation) comparison: ΨNGVBL>ΨmaxDetermining a high model uncertainty; ΨNGVBL≤ΨmaxA low model uncertainty is determined.
In step S103, a gain term is calculated according to the model uncertainty using an adaptive switching strategy, and the gain term is used to calculate the target state estimation value in a framework of a priori prediction-posterior update.
Specifically, step S103 specifically includes:
step S1: based on the determination of the uncertainty of the model at the current time K +1 in step S102, an adaptive switching strategy is used to calculate an innovation gain term K (K + 1):
in low model uncertainty case (Ψ)NGVBL≤Ψmax) The innovation gain term K (K +1) ═ KTanhThe calculation method comprises the following steps:
Figure BDA0002663486760000094
Figure BDA0002663486760000095
Figure BDA0002663486760000096
in case of high model uncertainty (Ψ)NGVBL>Ψmax) Using the nonlinear optimum Ψ obtained in step S101NGVBLSubstituted for ΨmaxSubstituted into the above formula KTanhThe optimal innovation gain term K (K +1) ═ K can be obtainedNGVBL：
KNGVBL＝P(k+1|k)H(k+1)TS(k+1)-1。
Step S2: and (4) estimating the motion state of the target in real time in an iterative frame of prior prediction and posterior update by using the innovation gain item K (K +1) calculated by the self-adaptive switching strategy in the step (S1), and specifically operating as follows. Target state variable at time k-0
Figure BDA0002663486760000097
And the state estimation covariance P (0|0) is iterated for initialization data, assuming that the state variables at time k and the posterior estimates of their covariance matrices are known
Figure BDA0002663486760000098
And P (k | k), specifically, step S2 operates in the following substeps:
step S21: calculating the prior estimation of the target state at the k +1 moment based on a preset target motion model and a radar measurement model
Figure BDA0002663486760000101
Radar measurement prior estimation
Figure BDA0002663486760000102
And a prior state estimation covariance matrix P (k +1| k):
Figure BDA0002663486760000103
Figure BDA0002663486760000104
Figure BDA0002663486760000105
wherein the content of the first and second substances,
Figure BDA0002663486760000106
and u is the control input matrix and control input variables and Q is the process noise covariance.
Step S22: calculating a priori measurement error (i.e. innovation) by using a target measurement z (k +1) scanned by the radar at the time k + 1:
Figure BDA0002663486760000107
calculating a blending error term, here using ez(k | k) represents the posterior measurement error at time k ·ABSMeans taking the absolute value element by element for the vector,
Figure BDA0002663486760000108
and
Figure BDA0002663486760000109
is an attenuation factor with a value in the interval (0, 1):
Figure BDA00026634867600001010
Figure BDA00026634867600001011
calculating a new information covariance matrix S (k + 1):
S(k+1)＝H(k+1)P(k+1|k)H(k+1)T+R(k+1)
the above equations are substituted into the adaptive switching policy calculation K (K +1) in step S1.
Step S23: calculating the posterior estimation of the target state by using the prior predicted values of the items in the step S21 and the innovation gain item in the step S22
Figure BDA00026634867600001012
And a posterior state estimation covariance matrix P (k +1| k + 1):
Figure BDA00026634867600001013
P(k+1|k+1)＝[I-K(k+1)H(k+1)]P(k+1|k)[I-K(k+1)H(k+1)]T+K(k+1)R(k+1)K(k+1)T
wherein the content of the first and second substances,
Figure BDA00026634867600001014
is a unit matrix and R represents the measurement noise covariance.
Step S3: and repeating the sequential iteration process of the step S2 for the k- th 1,2 and … radar scanning echoes until the radar system judges that the track is finished. Therefore, the real-time accurate estimation of the radar target state under the uncertain condition of the model is realized.
The method for estimating a state of a radar target by using a smooth variable structure filter based on a nonlinear optimal smoothing layer strategy is further described below by a specific embodiment, and an operation flow chart of the method is shown in fig. 2, specifically as follows:
maneuvering target tracking is a typical scenario for model uncertainty problems. The simulation scene of tracking and filtering of the 2-D millimeter wave radar on the single dynamic target under the automatic driving scene is considered. The radar is established at the coordinate origin, and the maneuvering path of the target is shown in figure 3. In this embodiment, the SVSF method based on the nonlinear optimal smoothing layer strategy (denoted as NGVBL-SVSF) provided by the present invention, the standard kalman filtering method (KF), the standard smooth variable structure filtering method (SVSF), the conventional SVSF method based on the modified handover function (denoted as Tanh-SVSF), and the conventional SVSF method based on the linear optimal smoothing layer parameter (denoted as NGVBL-SVSF) are compared in a simulation manner. The average results of 10000 monte carlo experiments were used as comparative data.
Simulated radar target data is generated using the simulation parameters of table 1. The target state variable is defined as a position and a speed in an X-Y coordinate axis, namely X ═ X Y vx vy]T(ii) a The radar measurement variable is defined as the target position, i.e. z ═[x y]TEstimating the target state by adopting a uniform motion model (CV), namely:
Figure BDA0002663486760000111
the measurement model matrix is:
Figure BDA0002663486760000112
TABLE 1 Radar target tracking scene parameters
Figure BDA0002663486760000113
Specific radar parameters, target state parameters, and filter algorithm parameters are given below:
target state variable at time k-0
Figure BDA0002663486760000114
And the state estimation covariance P (0|0) is iterated for initialization data, assuming that the state variables at time k and the posterior estimates of their covariance matrices are known
Figure BDA0002663486760000115
And P (k | k), operating according to the following steps:
1) calculating the prior estimation of the target state at the k +1 moment based on a preset target motion model and a radar measurement model
Figure BDA0002663486760000121
Radar measurement prior estimation
Figure BDA0002663486760000122
And a prior state estimation covariance matrix P (k +1| k):
Figure BDA0002663486760000123
Figure BDA0002663486760000124
Figure BDA0002663486760000125
2) calculating a gain term K (K +1) using an adaptive switching strategy:
firstly, calculating a nonlinear optimal smooth layer parameter psiNGVBL：
Figure BDA0002663486760000126
Figure BDA0002663486760000127
Figure BDA0002663486760000128
Fitting the nonlinear optimal smoothing layer parameter ΨNGVBLWith a predetermined smoothing layer parameter ΨmaxAnd (3) comparison: ΨNGVBL>ΨmaxDetermining a high model uncertainty; ΨNGVBL≤ΨmaxA low model uncertainty is determined.
If the low model uncertainty condition is determined, the innovation gain term K (K +1) is equal to KTanhThe calculation method comprises the following steps:
Figure BDA0002663486760000129
Figure BDA00026634867600001210
Figure BDA00026634867600001211
on the contrary, if the model uncertainty is determined to be high, the innovation gain term K (K +1) is KNGVBLThe calculation method comprises the following steps:
KNGVBL＝P(k+1|k)H(k+1)TS(k+1)-1
3) utilizing the innovation gain term psi obtained in the step 2)NGVBLCalculating a posterior estimate of the target state
Figure BDA00026634867600001212
And a posterior state estimation covariance matrix P (k +1| k + 1):
Figure BDA00026634867600001213
P(k+1|k+1)＝[I-K(k+1)H(k+1)]P(k+1|k)[I-K(k+1)H(k+1)]T+K(k+1)R(k+1)K(k+1)T
and repeating the sequential iteration process for the k- th 1,2, … and 200 radar scanning echoes until the target track is terminated. Therefore, the real-time accurate estimation of the radar target state under the uncertain condition of the model is realized.
FIG. 4 shows the coordinate error and velocity error of the target state estimate as a function of scan time; FIG. 5 compares the buffeting magnitude of the state estimates for the four SVSF methods. The Root Mean Square Error (RMSE) for 10000 monte carlo experiments is given in table 2.
TABLE 2 State estimation root mean square error of model uncertain targets
Figure BDA0002663486760000131
As can be seen from fig. 4 and 5, the NGVBL-SVSF method provided in the embodiment of the present invention achieves the best tracking accuracy. Compared with standard Kalman Filtering (KF), the NGVBL-SVSF method is more robust in tracking performance when the target moves flexibly (the error of the peak coordinate is reduced by more than 2/3). Compared with other three SVSF, the NGVBL-SVSF method integrates the advantages of the nonlinear switching function of Tanh-SVSF in buffeting suppression and the advantages of GVBL-SVSF in parameter optimality. Specifically, the target moves at a constant speed in 0-3s and 17.5-20s, and the model uncertainty is small, so that the NGVBL-SVSF benefits from nonlinear optimal smooth layer parameters and is obviously superior to standard SVSF and Tanh-SVSF methods adopting fixed parameters, and even approaches to optimal Bayesian estimation (namely a KF result); at 14.5-20s and 0-5s, the buffeting phenomenon is very serious (as shown in FIG. 5), and the NGVBL-SVSF benefits from the nonlinear switching function and achieves better buffeting suppression effect, so that the estimation of the target state, particularly the speed, is more accurate. In conclusion, the tracking error of the method provided by the invention is obviously superior to that of the traditional method, and the more robust and accurate radar target state estimation can be realized under the condition of uncertain model.
In conclusion, theoretical analysis and experimental results show that the method provided by the embodiment of the invention can obviously improve the radar target state estimation precision, ensure the filtering robustness under the uncertain model condition, and has good application value. The invention has the characteristics and the beneficial effects compared with the prior method that:
(1) avoid the parameter sensitivity
The performance of the conventional SVSF method depends on the accuracy of the preset smoothing layer parameters (see related art 1 and related art 2). The invention derives a nonlinear optimal smooth layer parameter based on a nonlinear switching function and a minimum mean square error criterion, and the parameter can ensure the optimality of state estimation errors under the condition of low model uncertainty. Therefore, compared with the conventional SVSF adopting fixed smooth layer parameters, the method can avoid the performance deterioration caused by unreasonable preset parameter values.
(2) Effectively inhibit the problem of buffeting
The traditional SVSF method adopts a sign function or a piecewise linear saturation function as a switching function, and can generate obvious buffeting. The method adopts the nonlinear hyperbolic tangent function as the switching function, can effectively reduce the disturbance of the observation noise component in the innovation item on the gain item, and thus inhibits the buffeting amplitude of state estimation. Therefore, compared with the traditional two switching functions, the method can obtain a target state estimation result with higher precision.
(3) High tracking precision
The method disclosed by the invention integrates the advantages of the existing method (related technology 3) in the aspect of parameter optimality and the benefits of the existing method (related technology 2) in the problem of buffeting suppression, designs a gain term calculation criterion adaptively switched along with model uncertainty, deduces time-varying nonlinear optimal smooth layer parameters based on a nonlinear switching function, and complementarily utilizes the optimality of the time-varying smooth layer parameters under the condition of low uncertainty and the buffeting suppression of the nonlinear switching function under the condition of high uncertainty, so that better target tracking accuracy is obtained than that of the existing methods (related technology 2 and related technology 3).
(4) Good tracking robustness
The method provided by the invention can adaptively judge the uncertainty of the model. By calculating the nonlinear optimal smooth layer parameters in real time and comparing the parameters with preset values, the uncertainty of the model at the current moment can be judged. Under the condition of high uncertainty, a standard gain term calculation method based on a nonlinear switching function and fixed smooth layer parameters is used, and the boundedness of the posterior estimation error is ensured. Therefore, compared with the traditional Bayes method (such as Kalman filtering), the method provided by the invention can keep more robust target tracking performance under the uncertain condition of the model.
According to the smoothing variable structure filtering method based on the nonlinear optimal smoothing layer strategy provided by the embodiment of the invention, the gain item is calculated by adopting the adaptive switching strategy based on the nonlinear optimal smoothing layer parameters, so that the optimality of a tracking algorithm and a system under low model uncertainty can be realized, and meanwhile, the robustness under high uncertainty and excellent buffeting suppression characteristics are ensured, so that better target state tracking accuracy is obtained, and the method has higher engineering application value.
Next, a proposed smoothing variable structure filtering system based on a nonlinear optimal smoothing layer strategy according to an embodiment of the present invention is described with reference to the drawings.
Fig. 6 is a schematic structural diagram of a smoothing variable structure filtering system based on a nonlinear optimal smoothing layer strategy according to an embodiment of the present invention.
As shown in fig. 6, the smoothing variable structure filtering system 10 based on the nonlinear optimal smoothing layer strategy includes: a first calculation module 100, a comparison module 200 and a second calculation module 300.
The first calculation module 100 is configured to calculate a nonlinear optimal smoothing layer parameter in real time under a minimum mean square error criterion based on a nonlinear switching function; the comparison module 200 is configured to compare the nonlinear optimal smoothing parameter with a preset smoothing layer parameter to determine the uncertainty of the current model; the second calculation module 300 is configured to calculate a gain term according to the uncertainty of the current model by using an adaptive switching strategy, and calculate an estimated value of the target state in a framework of a priori prediction and a posteriori update by using the gain term. The system 10 of the embodiment of the invention can obviously improve the radar target state estimation precision, ensure the filtering robustness under the uncertain condition of the model and has good application value.
Further, in an embodiment of the present invention, the calculation formula of the nonlinear optimal smoothing layer parameter is:
Figure BDA0002663486760000151
Figure BDA0002663486760000152
Figure BDA0002663486760000153
wherein artan (-) is an inverse hyperbolic tangent function defined on each element of the matrix;
Figure BDA0002663486760000154
indicating the k +1 th frame radar measurement matrix
Figure BDA0002663486760000155
The full-rank blocking submatrix of (1), wherein m and n are the dimensions of the system state variable and the observation variable, respectively;
Figure BDA0002663486760000156
and
Figure BDA0002663486760000157
is a block submatrix of a prior state estimation error covariance matrix P (k +1| k); e.g. of the typez(k +1| k) is the observation innovation term; s (k +1) is an innovation covariance matrix; ezAnd EyIs a mixing error term;
Figure BDA0002663486760000158
is to the state transition matrix
Figure BDA0002663486760000159
Transformation state transition matrix after introduction of transformation matrix T
Figure BDA00026634867600001510
Representing the main diagonal element as a diagonal matrix of vector a.
Further, in one embodiment of the present invention, the comparison module 200 is further configured to determine when ΨNGVBL>ΨmaxWhen the model uncertainty is high, the uncertainty of the current model is judged to be high, wherein psiNGVBLFor a non-linear optimal smoothing layer parameter, ΨmaxThe parameters are preset smooth layer parameters; when t isNGVBL≤ΨmaxJudging the uncertainty of the current model as low model uncertainty;
under low model uncertainty conditions, the gain term is calculated as:
Figure BDA00026634867600001511
Figure BDA00026634867600001512
Figure BDA00026634867600001513
under the condition of high model uncertainty, the calculation formula of the gain term is as follows:
K(k+1)＝KNGVBL，
KNGVBL＝P(k+1|k)H(k+1)TS(k+1)-1。
further, in an embodiment of the present invention, the second calculating module 300 is further configured to target the state variable at the time when k is 0
Figure BDA0002663486760000161
And the covariance P (0|0) of the state estimation is used as initialization data, and the state variable at the moment of k +1 and the posterior estimation of the covariance matrix thereof are calculated in an iterative way
Figure BDA0002663486760000162
And P (k +1| k +1), k being 0,1,2, …, until the radar system determines that the track is finished, specifically including:
1) calculating the prior estimation of the target state at the k +1 moment based on a preset target motion model and a radar measurement model
Figure BDA0002663486760000163
Radar measurement prior estimation
Figure BDA0002663486760000164
And a prior state estimation covariance matrix P (k +1| k):
Figure BDA0002663486760000165
Figure BDA0002663486760000166
Figure BDA0002663486760000167
wherein the content of the first and second substances,
Figure BDA0002663486760000168
and u is the control input matrix and control input variable, Q is the process noise covariance;
2) and (3) calculating a priori measurement error by using a target measurement z (k +1) scanned by the radar at the k +1 moment:
Figure BDA0002663486760000169
calculating a blending error term using ez(k | k) represents the posterior measurement error at time k ·ABSMeans taking the absolute value element by element for the vector,
Figure BDA00026634867600001610
and
Figure BDA00026634867600001611
is an attenuation factor with a value in the interval (0, 1):
Figure BDA00026634867600001612
Figure BDA00026634867600001613
calculating a new information covariance matrix S (k + 1):
S(k+1)＝H(k+1)P(k+1|k)H(k+1)T+R(k+1)，
substituting a priori measurement error calculation formula, a mixed error term calculation formula and an innovation covariance matrix calculation formula into a self-adaptive switching strategy to calculate a gain term K (K + 1);
3) calculating the posterior estimation of the target state by using each item of prior predicted value in 1) and gain item K (K +1) in 2)
Figure BDA00026634867600001614
And a posterior state estimation covariance matrix P (k +1| k + 1):
Figure BDA0002663486760000171
P(k+1|k+1)＝[I-K(k+1)H(k+1)]P(k+1|k)[I-K(k+1)H(k+1)]T+K(k+1)R(k+1)K(k+1)Twherein the content of the first and second substances,
Figure BDA0002663486760000172
is a unit matrix and R represents the measurement noise covariance.
It should be noted that the foregoing explanation of the embodiment of the smooth-varying structure filtering method based on the nonlinear optimal smooth layer policy is also applicable to the smooth-varying structure filtering system based on the nonlinear optimal smooth layer policy in this embodiment, and is not repeated here.
According to the smoothing variable structure filtering system based on the nonlinear optimal smoothing layer strategy provided by the embodiment of the invention, the gain item is calculated by adopting the adaptive switching strategy based on the nonlinear optimal smoothing layer parameters, so that the optimality of a tracking algorithm and the system under low model uncertainty can be realized, and meanwhile, the robustness under high uncertainty and excellent buffeting suppression characteristics are ensured, so that better target state tracking accuracy is obtained, and the system has higher engineering application value.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims (10)

1. A smooth variable structure filtering method based on a nonlinear optimal smooth layer strategy is characterized by comprising the following steps:
calculating nonlinear optimal smooth layer parameters in real time under the minimum mean square error criterion based on a nonlinear switching function;
comparing the nonlinear optimal smooth parameter with a preset smooth layer parameter to judge the uncertainty of the current model; and
and calculating a gain term by adopting a self-adaptive switching strategy according to the uncertainty of the current model, and calculating a target state estimation value in a priori prediction-posterior updating frame by utilizing the gain term.
2. The method of claim 1, wherein the non-linear optimal smoothing layer parameter is calculated by:
Figure FDA0002663486750000011
Figure FDA0002663486750000012
Figure FDA0002663486750000013
wherein artan (-) is an inverse hyperbolic tangent function defined on each element of the matrix;
Figure FDA0002663486750000014
indicating the k +1 th frame radar measurement matrix
Figure FDA0002663486750000015
The full-rank blocking submatrix of (1), wherein m and n are the dimensions of the system state variable and the observation variable, respectively;
Figure FDA0002663486750000016
and
Figure FDA0002663486750000017
is a block submatrix of a prior state estimation error covariance matrix P (k +1| k); e.g. of the typez(k +1| k) is the observation innovation term; s (k +1) is an innovation covariance matrix; ezAnd EyIs a mixing error term;
Figure FDA0002663486750000018
is to the state transition matrix
Figure FDA0002663486750000019
Transformation state transition matrix after introduction of transformation matrix T
Figure FDA00026634867500000110
Figure FDA00026634867500000111
Representing the main diagonal element as a diagonal matrix of vector a.
3. The method of claim 1, wherein comparing the non-linear optimal smoothing parameter with a preset smoothing layer parameter to determine the uncertainty of the current model, further comprises:
when t isNGVBL>ΨmaxIn time, it is determined as a high model uncertainty, where ΨNGVBLFor a non-linear optimal smoothing layer parameter, ΨmaxThe parameters are preset smooth layer parameters;
when t isNGVBL≤ΨmaxWhen it is determined to be low model uncertainty.
4. The method of claim 3, wherein based on the determined magnitude of the current model uncertainty, an adaptive handover strategy is used to calculate the gain term, expressed as:
under low model uncertainty conditions, the gain term is calculated as:
Figure FDA0002663486750000021
Figure FDA0002663486750000022
Figure FDA0002663486750000023
under the condition of high model uncertainty, the calculation formula of the gain term is as follows:
K(k+1)＝KNGVBL，
KNGVBL＝P(k+1|k)H(k+1)TS(k+1)-1。
5. the method of claim 1, wherein using the gain term to compute the target state estimate in a framework of a priori prediction-a posteriori updating comprises:
target state variable at time k-0
Figure FDA0002663486750000024
And the covariance P (0|0) of the state estimation is used as initialization data, and the state variable at the moment of k +1 and the posterior estimation of the covariance matrix thereof are calculated in an iterative way
Figure FDA0002663486750000025
And P (k +1| k +1), k being 0,1,2, …, until the radar system judges that the track is finished, the specific steps are as follows:
5-1) calculating the prior estimation of the target state at the k +1 moment based on a preset target motion model and a radar measurement model
Figure FDA0002663486750000026
Radar measurement prior estimation
Figure FDA0002663486750000027
And a prior state estimation covariance matrix P (k +1| k):
Figure FDA0002663486750000028
Figure FDA0002663486750000029
Figure FDA00026634867500000210
wherein the content of the first and second substances,
Figure FDA00026634867500000211
and u is the control input matrix and control input variable, Q is the process noise covariance;
5-2) calculating prior measurement error by using target measurement z (k +1) scanned by the radar at the k +1 moment:
Figure FDA00026634867500000212
calculating a blending error term using ez(k | k) represents the posterior measurement error at time k ·ABSMeans taking the absolute value element by element for the vector,
Figure FDA00026634867500000213
and
Figure FDA00026634867500000214
is an attenuation factor with a value in the interval (0, 1):
Figure FDA00026634867500000215
Figure FDA0002663486750000031
calculating a new information covariance matrix S (k + 1):
S(k+1)＝H(k+1)P(k+1|k)H(k+1)T+R(k+1)，
substituting a priori measurement error calculation formula, a mixed error term calculation formula and an innovation covariance matrix calculation formula into a self-adaptive switching strategy to calculate a gain term K (K + 1);
5-3) calculating the posterior estimation of the target state by utilizing each item of prior predicted value in 5-2) and the gain item K (K +1) in 5-3)
Figure FDA0002663486750000032
And a posterior state estimation covariance matrix P (k +1| k + 1):
Figure FDA0002663486750000033
P(k+1|k+1)＝[I-K(k+1)H(k+1)]P(k+1|k)[I-K(k+1)H(k+1)]T+K(k+1)R(k+1)K(k+1)T
wherein the content of the first and second substances,
Figure FDA0002663486750000034
is a unit matrix and R represents the measurement noise covariance.
6. A smooth variable structure filtering system based on a nonlinear optimal smoothing layer strategy, comprising:
the first calculation module is used for calculating nonlinear optimal smooth layer parameters in real time under the minimum mean square error criterion based on a nonlinear switching function;
the comparison module is used for comparing the nonlinear optimal smooth parameter with a preset smooth layer parameter so as to judge the uncertainty of the current model; and
and the second calculation module is used for calculating a gain term by adopting a self-adaptive switching strategy according to the uncertainty of the current model and calculating the estimated value of the target state in a frame of prior prediction-posterior update by utilizing the gain term.
7. The system of claim 6, wherein the non-linear optimal smoothing layer parameter is calculated by:
Figure FDA0002663486750000035
Figure FDA0002663486750000036
Figure FDA0002663486750000037
wherein artan (-) is an inverse hyperbolic tangent function defined on each element of the matrix;
Figure FDA0002663486750000038
indicating the k +1 th frame radar measurement matrix
Figure FDA0002663486750000039
The full-rank blocking submatrix of (1), wherein m and n are the dimensions of the system state variable and the observation variable, respectively;
Figure FDA0002663486750000041
and
Figure FDA0002663486750000042
is a block submatrix of a prior state estimation error covariance matrix P (k +1| k); e.g. of the typez(k +1| k) is the observation innovation term; s (k +1) is an innovation covariance matrix; ezAnd EyIs a mixing error term;
Figure FDA0002663486750000043
is to the state transition matrix
Figure FDA0002663486750000044
Transformation state transition matrix after introduction of transformation matrix T
Figure FDA0002663486750000045
Figure FDA0002663486750000046
Representing the main diagonal element as a diagonal matrix of vector a.
8. The system of claim 6, wherein the contrast module is further configured to compare ΨNGVBL>ΨmaxIn time, it is determined as a high model uncertainty, where ΨNGVBLFor a non-linear optimal smoothing layer parameter, ΨmaxThe parameters are preset smooth layer parameters; when t isNGVBL≤ΨmaxWhen it is determined to be low model uncertainty.
9. The system of claim 6, wherein the gain term is calculated by the formula:
Figure FDA0002663486750000047
Figure FDA0002663486750000048
Figure FDA0002663486750000049
under the condition of high model uncertainty, the calculation formula of the gain term is as follows:
K(k+1)＝KNGVBL，
KNGVBL＝P(k+1|k)H(k+1)TS(k+1)-1。
10. the system of claim 6, wherein the second calculation module is further configured to target the state variable at time k-0
Figure FDA00026634867500000410
And the covariance P (0|0) of the state estimation is used as initialization data, and the state variable at the moment of k +1 and the posterior estimation of the covariance matrix thereof are calculated in an iterative way
Figure FDA00026634867500000411
And P (k +1| k +1), k being 0,1,2, …, until the radar system determines that the track is finished, specifically including:
10-1) calculating the prior estimation of the target state at the moment k +1 based on a preset target motion model and a radar measurement model
Figure FDA00026634867500000412
Radar measurement prior estimation
Figure FDA00026634867500000413
And a prior state estimation covariance matrix P (k +1| k):
Figure FDA00026634867500000414
Figure FDA00026634867500000415
Figure FDA00026634867500000416
wherein the content of the first and second substances,
Figure FDA0002663486750000051
and u is the control input matrix and control input variable, Q is the process noise covariance;
10-2) calculating prior measurement error by using target measurement z (k +1) scanned by the radar at the k +1 moment:
Figure FDA0002663486750000052
calculating a blending error term using ez(k | k) represents the posterior measurement error at time k ·ABSMeans taking the absolute value element by element for the vector,
Figure FDA0002663486750000053
and
Figure FDA0002663486750000054
is an attenuation factor with a value in the interval (0, 1):
Figure FDA0002663486750000055
Figure FDA0002663486750000056
calculating a new information covariance matrix S (k + 1):
S(k+1)＝H(k+1)P(k+1|k)H(k+1)T+R(k+1)，
substituting a priori measurement error calculation formula, a mixed error term calculation formula and an innovation covariance matrix calculation formula into a self-adaptive switching strategy to calculate a gain term K (K + 1);
10-3) calculating the posterior estimation of the target state by using each item of prior predicted value in 10-1) and a gain item K (K +1) in 10-2)
Figure FDA0002663486750000057
And a posterior state estimation covariance matrix P (k +1| k + 1):
Figure FDA0002663486750000058
P(k+1|k+1)＝[I-K(k+1)H(k+1)]P(k+1|k)[I-K(k+1)H(k+1)]T+K(k+1)R(k+1)K(k+1)T
wherein the content of the first and second substances,
Figure FDA0002663486750000059
is a unit matrix and R represents the measurement noise covariance.
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